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R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 17 Dec 2007 11:55:22 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/17/t1197916821khev31dso1iy2mt.htm/, Retrieved Mon, 17 Dec 2007 19:40:31 +0100

User-defined keywords:

Multiple Regression

Dataseries X:

» Textbox « » Textfile « » CSV «

103,1 98,6 98,1 98,6 100,6 98 101,1 98 103,1 106,8 111,1 106,8 95,5 96,6 93,3 96,7 90,5 100,1 100 100,2 90,9 107,7 108 107,7 88,8 91,5 70,4 92 90,7 97,8 75,4 98,4 94,3 107,4 105,5 107,4 104,6 117,5 112,3 117,7 111,1 105,6 102,5 105,7 110,8 97,4 93,5 97,5 107,2 99,5 86,7 99,9 99 98 95,2 98,2 99 104,3 103,8 104,5 91 100,6 97 100,8 96,2 101,1 95,5 101,5 96,9 103,9 101 103,9 96,2 96,9 67,5 99,6 100,1 95,5 64 98,4 99 108,4 106,7 112,7 115,4 117 100,6 118,4 106,9 103,8 101,2 108,1 107,1 100,8 93,1 105,4 99,3 110,6 84,2 114,6 99,2 104 85,8 106,9 108,3 112,6 91,8 115,9 105,6 107,3 92,4 109,8 99,5 98,9 80,3 101,8 107,4 109,8 79,7 114,2 93,1 104,9 62,5 110,8 88,1 102,2 57,1 108,4 110,7 123,9 100,8 127,5 113,1 124,9 100,7 128,6 99,6 112,7 86,2 116,6 93,6 121,9 83,2 127,4 98,6 100,6 71,7 105 99,6 104,3 77,5 108,3 114,3 120,4 89,8 125 107,8 107,5 80,3 111,6 101,2 102,9 78,7 106,5 112,5 125,6 93,8 130,3 100,5 107,5 57,6 115 93,9 108,8 60,6 116,1 116,2 128,4 91 134 112 121,1 85,3 126,5 106,4 119,5 77,4 125,8 95,7 128,7 77,3 136,4 96 108,7 68,3 114,9 95,8 105,5 69,9 110,9 103 119,8 81,7 125,5 102,2 111,3 75,1 116,8 98,4 110,6 69,9 116,8 111,4 120,1 84 125,5 86,6 97,5 54,3 104,2 91,3 107,7 60 115,1 107,9 127,3 89,9 132,8 101,8 117,2 77 123,3 104,4 119,8 85,3 124,8 93,4 116,2 77,6 122 100,1 111 69,2 117,4 98,5 112,4 75,5 117,9 112,9 130,6 85,7 137,4 101,4 109,1 72,2 114,6 107,1 118,8 79,9 124,7 110,8 123,9 85,3 129,6 90,3 101,6 52,2 109,4 95,5 112,8 61,2 120,9 111,4 128 82,4 134,9 113 129,6 85,4 136,3 107,5 125,8 78,2 133,2 95,9 119,5 70,2 127,2 106,3 115,7 70,2 122,7 105,2 113,6 69,3 120,5 117,2 129,7 77,5 137,8 106,9 112 66,1 119,1 108,2 116,8 69 124,3 110 126,3 75,3 134,3 96,1 112,9 58,2 121,7 100,6 115,9 59,7 125

Text written by user:

zonder externe invloeden

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Totale-Consumptiegoederen[t] = + 2.52721795203605 + 0.00505963680901596`Intermediaire-goederen`[t] + 0.117591019265851`Duurzame-consumptiegoederen`[t] + 0.85214723860919`Niet-duurzame-consumptiegoederen `[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 2.52721795203605 1.293398 1.9539 0.054388 0.027194 `Intermediaire-goederen` 0.00505963680901596 0.016589 0.305 0.761201 0.3806 `Duurzame-consumptiegoederen` 0.117591019265851 0.007167 16.4063 0 0 `Niet-duurzame-consumptiegoederen ` 0.85214723860919 0.010044 84.8444 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.996832156946681 R-squared 0.993674349122973 Adjusted R-squared 0.993424652377827 F-TEST (value) 3979.52463714607 F-TEST (DF numerator) 3 F-TEST (DF denominator) 76 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.815828659679967 Sum Squared Residuals 50.5838065485961 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 98.6 98.6062632238924 -0.00626322389244786 2 98 98.4350988465014 -0.435098846501362 3 106.8 107.122553830943 -0.322553830943246 4 96.6 96.3842933383098 0.215706661690198 5 100.1 100.129370318478 -0.0293703184780553 6 107.7 107.463226616897 0.236773383102613 7 91.5 89.6524674090382 1.84753259096183 8 97.8 95.7037781424034 2.09622185759662 9 107.4 106.930807662301 0.469192337699345 10 117.5 116.559657410116 0.940342589884038 11 105.6 105.214386197259 0.385613802741049 12 97.4 97.1669417762282 0.233058223771783 13 99.5 98.39426152537 1.10573847462996 14 98 97.9036458616602 0.0963541383397808 15 104.3 104.283456230584 0.0165437694155659 16 100.6 100.290415422251 0.309584577749482 17 101.1 100.736842071785 0.363157928214941 18 103.9 103.432287796176 0.467712203824399 19 96.9 95.8252137789838 1.07478622101625 20 95.5 94.4108011087774 1.08919889122258 21 108.4 111.612077543051 -3.21207754305075 22 117 115.834989629269 1.16501037073069 23 103.8 107.085420770278 -3.28542077027753 24 100.8 103.833147897341 -3.03314789734113 25 110.6 110.586877253969 0.0131227460307282 26 104 104.212983183823 -0.212983183822974 27 112.6 112.633897141863 -0.0338971418628386 28 107.3 107.492692578522 -0.192692578521939 29 98.9 99.2217995519966 -0.321799551996616 30 109.8 109.757841829982 0.0421581700177028 31 104.9 104.765622880969 0.134377119030528 32 102.2 102.060179820227 0.139820179773248 33 123.9 123.589267411464 0.31073258853628 34 124.9 124.527013400349 0.372986599651123 35 112.7 112.527871660762 0.172128339237950 36 121.9 121.347930959090 0.552069040910341 37 100.6 100.932834276732 -0.332834276731603 38 104.3 104.432007712693 -0.132007712692878 39 120.4 120.183612795529 0.216387204471160 40 107.5 107.614837475882 -0.114837475881511 41 102.9 103.047347325210 -0.147347325209777 42 125.6 125.161249890965 0.438750109035257 43 107.5 107.805886601112 -0.305886601112124 44 108.8 109.062628018440 -0.262628018440281 45 128.4 128.003660476068 0.3963395239323 46 121.1 120.921036902086 0.178963097914429 47 119.5 119.367230816728 0.132769183271583 48 128.7 128.334094330203 0.365905669797204 49 108.7 108.956127417755 -0.256127417755243 50 105.5 105.734672166782 -0.234672166782047 51 119.8 119.600025262838 0.199974737161828 52 111.3 111.406195850336 -0.106195850336388 53 110.6 110.775495930280 -0.175495930279706 54 120.1 119.912985556345 0.187014443654634 55 97.5 98.1443171089103 -0.644317108910251 56 107.7 108.126771112568 -0.426771112568134 57 127.3 126.809738683029 0.490261316970575 58 117.2 117.166551983178 0.0334480168223722 59 119.8 119.433933356701 0.366066643298577 60 116.2 116.086814235349 0.113185764650535 61 111 111.213071942534 -0.213071942534451 62 112.4 112.371873564319 0.0281264356805221 63 130.6 130.261031883760 0.338968116239801 64 109.1 109.186410260078 -0.0864102600779904 65 118.8 118.727388148189 0.0726118518107436 66 123.9 123.556621777603 0.343378222396777 67 101.6 102.347262265413 -0.747262265413116 68 112.8 113.231584794218 -0.431584794218335 69 128 127.735023968446 0.264976031553612 70 129.6 129.288898579191 0.311101420808759 71 125.8 125.772758798339 0.0272412016609843 72 119.5 119.660455425572 -0.160455425572493 73 115.7 115.878413074645 -0.178413074644901 74 113.6 113.892291631875 -0.292291631875506 75 129.7 129.659400859503 0.0405991404973276 76 112 112.331595618747 -0.331595618747232 77 116.8 117.110352743238 -0.310352743237714 78 126.3 126.381755896961 -0.0817558969607134 79 112.9 113.563565309394 -0.663565309393533 80 115.9 116.574806091343 -0.674806091343205

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab')

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Software written by Ed van Stee & Patrick Wessa

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